Basic Math Examples

${(2 \sqrt{7} + 4)}^{2}$

Step 1

Rewrite ${(2 \sqrt{7} + 4)}^{2}$ as $(2 \sqrt{7} + 4) (2 \sqrt{7} + 4)$ .

$(2 \sqrt{7} + 4) (2 \sqrt{7} + 4)$

Step 2

Expand $(2 \sqrt{7} + 4) (2 \sqrt{7} + 4)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 \sqrt{7} (2 \sqrt{7} + 4) + 4 (2 \sqrt{7} + 4)$

Step 2.2

Apply the distributive property.

$2 \sqrt{7} (2 \sqrt{7}) + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7} + 4)$

Step 2.3

Apply the distributive property.

$2 \sqrt{7} (2 \sqrt{7}) + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2 \sqrt{7} (2 \sqrt{7})$ .

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Step 3.1.1.1

Multiply $2$ by $2$ .

$4 \sqrt{7} \sqrt{7} + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.1.2

Raise $\sqrt{7}$ to the power of $1$ .

$4 ({\sqrt{7}}^{1} \sqrt{7}) + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.1.3

Raise $\sqrt{7}$ to the power of $1$ .

$4 ({\sqrt{7}}^{1} {\sqrt{7}}^{1}) + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.1.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 {\sqrt{7}}^{1 + 1} + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.1.5

Add $1$ and $1$ .

$4 {\sqrt{7}}^{2} + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.2

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 3.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$4 {(7^{\frac{1}{2}})}^{2} + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 \cdot 7^{\frac{1}{2} \cdot 2} + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.2.3

Combine $\frac{1}{2}$ and $2$ .

$4 \cdot 7^{\frac{2}{2}} + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.2.4

Cancel the common factor of $2$ .

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Step 3.1.2.4.1

Cancel the common factor.

$4 \cdot 7^{\frac{2}{2}} + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.2.4.2

Rewrite the expression.

$4 \cdot 7^{1} + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.2.5

Evaluate the exponent.

$4 \cdot 7 + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.3

Multiply $4$ by $7$ .

$28 + 2 \sqrt{7} \cdot 4 + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.4

Multiply $4$ by $2$ .

$28 + 8 \sqrt{7} + 4 (2 \sqrt{7}) + 4 \cdot 4$

Step 3.1.5

Multiply $2$ by $4$ .

$28 + 8 \sqrt{7} + 8 \sqrt{7} + 4 \cdot 4$

Step 3.1.6

Multiply $4$ by $4$ .

$28 + 8 \sqrt{7} + 8 \sqrt{7} + 16$

Step 3.2

Add $28$ and $16$ .

$44 + 8 \sqrt{7} + 8 \sqrt{7}$

Step 3.3

Add $8 \sqrt{7}$ and $8 \sqrt{7}$ .

$44 + 16 \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$44 + 16 \sqrt{7}$

Decimal Form:

$86.33202097 \dots$